{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jacobi package examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This package calculates a few orthogonal polynomials such as Jacobi polynomials $P_n^{\\alpha,\\beta}(x)$, Chebyshev polynomials of the first and second kinds, $T_n(x)$ and $U_n(x)$ and Legendre Polynomials $P_n(x) = P_n^{0,0}(x)$.\n",
    "\n",
    "The polynomials can be calculated pointwise or a `Poly` structure can be obtained, which is basically made up of the polynomial coefficients.\n",
    "\n",
    "The respective derivatives can also be calculated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pointwise calculation of polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Jacobi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the Jacobi polynomial $P_5^{0.2, 0.1}(0.3)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3780304524166406"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 0.3\n",
    "a = 0.2\n",
    "b = 0.1\n",
    "m = 5\n",
    "jacobi(x, m, a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The derivative $\\left.\\frac{dP_5^{0.2, 0.1}(x)}{dx}\\right|_{x=0.3}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.4343764194492186"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "djacobi(x, m, a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Legendre, Chebyshev (first and second kind) are calculated as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.345386\n",
       " 0.99888 \n",
       " 1.01376 "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1 = legendre(x, m) # Legendre polynomial of degree m\n",
    "y2 = chebyshev(x, m) # Chebyshev polynomial of first kind of degree m\n",
    "y3 = chebyshev2(x, m) # Chebyshev polynomial of second kind of degree m\n",
    "[y1, y2, y3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the respective derivatives:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " -0.168562\n",
       "  0.248   \n",
       " -1.344   "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1 = dlegendre(x, m) # Derivative of Legendre polynomial of degree m\n",
    "y2 = dchebyshev(x, m) # Derivative of Chebyshev polynomial of first kind of degree m\n",
    "y3 = dchebyshev2(x, m) # Derivative ofChebyshev polynomial of second kind of degree m\n",
    "[y1, y2, y3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes it is useful to calculate the coefficients of the polynomials. The functions with prefix `poly_` return a Poly object available in the [package Polynomials](https://github.com/Keno/Polynomials.jl).\n",
    "\n",
    "The naming follows the pointwise calculation of polynomials already described above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(5x - 20x^3 + 16x^5)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Polynomials\n",
    "\n",
    "T5 = poly_chebyshev(5, Int, :x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "Polynomials must have same variable\nwhile loading In[10], in expression starting on line 1",
     "output_type": "error",
     "traceback": [
      "Polynomials must have same variable\nwhile loading In[10], in expression starting on line 1",
      "",
      " in * at /home/pjabardo/.julia/v0.3/Polynomials/src/Polynomials.jl:174",
      " in poly_chebyshev at /home/pjabardo/software/julia/Jacobi.jl/src/polynomials.jl:16"
     ]
    }
   ],
   "source": [
    "T8 = poly_chebyshev(8, Float64, :y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(1 - 32x^2 + 160x^4 - 256x^6 + 128x^8)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T4 = poly_chebyshev(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(-16x + 32x^3)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dT4dx = poly_dchebyshev(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(6x - 32x^3 + 32x^5)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U5 = poly_chebyshev2(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(6 - 96x^2 + 160x^4)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dU5dx = poly_dchebyshev2(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(-0.3125 + 6.5625x^2 - 19.6875x^4 + 14.4375x^6)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P6 = poly_legendre(6) # Legendre Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(13.125x - 78.75x^3 + 86.625x^5)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dP6 = polyder(P6)# Derivative using Polynomials Package\n",
    "dp6b = poly_dlegendre(6)  # Syntatic sugar calling the above line.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(0.0)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "err = dP6 - dp6b  # Both procedures above should be the same!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(-0.024746232255859372 - 2.4416546568652344x + 0.5967953141894532x^2 + 22.727281485986328x^3 - 1.9930645195800785x^4 - 51.4035174487207x^5 + 1.5947440682714844x^6 + 32.57834310897459x^7)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P7ab = poly_jacobi(7, a, b) # Jacobi polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Poly(-2.4416546568652344 + 1.1935906283789064x + 68.18184445795899x^2 - 7.972258078320314x^3 - 257.0175872436035x^4 + 9.568464409628906x^5 + 228.04840176282215x^6)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dP7abdx = poly_djacobi(7, a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating the polynomials at several points\n",
    "\n",
    "Often, it is necessary to calculate polynomials at several points. As syntatic sugar a few functions are available to make that easy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Loading help data...\n"
     ]
    }
   ],
   "source": [
    "using PyPlot # Seeing is believing ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = linspace(-1.0, 1.0, 401);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f77c9ec0ba8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 = chebyshev(x, 8);\n",
    "plot(x, y1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is the mutating function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f77b71f3da0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f77b7133080>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y2 = zeros(x);\n",
    "chebyshev!(x, 5, y2)\n",
    "plot(x, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same thing is implemented for Jacobi and Legendre polynomials and their derivative:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f77b7162a20>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f77b6f5fb00>\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f77b6f5fe48>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y3 = jacobi(x, 4, -0.5, 0.5)\n",
    "y4 = djacobi(x, 4, -0.5, 0.5)\n",
    "plot(x, y3, \"b-\", x, y4, \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zeros of polynomials\n",
    "\n",
    "oThe functions starting with suffix `_zero` calculate the zeros of the polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/D2zdap8xBM1NN8kRmhxHIHKWt98GMjNlFMFO7r8f2LULOHFCdSVkNAZbP7Bj6zzr18vGz/feq7qSwHvwQenYXrqkuhIiMkJjI7BunfW3LezNwoVAUJB0pMlZOGPrBwZb5/noIyA7G0hIUF1J4C1ZIifqffih6kqIyAh/+IOEADuNIWiGDQPmzpVmBDlLS4u8qQkJ0efr2zbYBgcz2DpNezvwv/9rvzEEzYQJwLx5HEcgcoq33wby84FJk1RXoo+775atzNrbVVdCRmppkTlrvRZD2jbYhocz2DrNpk1y686uwRaQW5IffwycO6e6EiLSU0ODvFG34xiC5u67gaYmYNs21ZWQkbRgqxfbBtuICAZbp/nDH4CJE4EZM1RXop/775cZ4j/8QXUlRKSndevkxLH771ddiX5mzpSxMY4jOEtrK4OtT9ixdZ4NG2QLGbvs9dib0aNlLu2DD1RXQkR6+uADIDcXGDdOdSX6cbmka8tg6ywtLdJ81AuDLdnCkSNy4tiXv6y6Ev0tWiTjCE1NqishIj20tMgYwqJFqivR3913A5WV8hpOzsBRBB8x2DrLJ5/IgsHbb1ddif4WLQLa2uTCR0T2s2GD3K51QrBdsAAIDeW2X07CYOsjBltn2bAByMsDYmNVV6K/KVNkNo3jCET29MEHwPTpQFKS6kr0FxMju73wVEXnaG3lKIJPGGydo7MT+PRT4M47VVdinEWL5EJw+bLqSogokDo6ZHGoE7q1mrvvBj77jNdsp2DH1kcMts7hdstpXE6Yr9UsWgRcvCgXAyKyj82bgQsXnBVs77pLxqu47ZczMNj6iMHWOT7+WE6xmTNHdSXGmTkTmDyZ4whEdvPBB7JtYVaW6kqMk5oKjBkjd97I/hhsfcRg6xwbNgBf+pIsHnMKl0s6Oh9+CHR3q66GiAKhuxv4/e+Br3/d3tsWXs/lkoW/DLbOwBlbHzHYOkNDg4wiOGkMQbNoEVBXBxQVqa6EiAJh1y7g1ClnjSFoFiwASkuB8+dVV0J6Y8fWRwy2zrBxo3Q5nBhs8/OBkSO5mpjILtatk7Gqm29WXYnxFiwAPB6ZMSZ7Y7D1EYOtM3z8MZCSAiQmqq7EeMHBsuhi3TrVlRBRIKxbJ7/TISGqKzHexInA1KkcR3ACHqnrIwZbZ9i4Ud7pO9U99wB79wKff666EiLyx8mTQFmZ/E471YIFDLZOwCN1fRQeLu8KuLDGvk6ckGN0589XXYk6d94pnVuOIxBZ2/r1QFAQsHCh6krUWbBAjtc9eVJ1JaSXzk7Zf50dWx+Eh8tjW5vaOkg/2izWLbeorUOluDigoIDjCERW98c/AnPnAsOHq65Endtuk8eNG9XWQfppbZVHBlsfaMGW4wj2tWmTHDs5apTqStT6ylfk9h2f60TW1NYGfPKJs8cQACA+HsjI4DiCnTHY+oHB1v42b3b2GILmnnvkwshTyIisafNmuVZ95SuqK1FPm7P1eFRXQnrQMhlnbH3AYGtvJ08CBw8y2AKyK8SUKZyzJbKqP/5RdnaZPl11JeotWCDrJw4eVF0J6UHLZOzY+oDB1t44X9vD5ZKu7bp17HIQWY3HI7+799zjrNPG+jJvniyI5X629sRg6wcGW3vbtAlIS+N8reYrX5Etv/bvV10JEQ1GZSVw9CjHEDRDhwKZmcDWraorIT1wxtYPDLb2tmkTxxCuduut8kKxfr3qSohoMNavl+uVtiMASdeWwdaeOGPrBwZb++J87Y3CwuTn8fHHqishosHYsEFGqvS80FvNvHlATY3M2pK9cBTBD9qLBIOt/WizV7feqrYOs7nzTmDbNqC5WXUlROSN1lZgyxb53aUe8+bJI7u29sNg64ewMHlksLWfzZs5X9ubO++UE102bVJdCRF5Y8sWoL2dwfZ68fGy28uWLaoroUDTZmy1u+p6sG2wdbnkHQGDrf1s3szdEHqTlARMnCi3NonI/DZsAMaNkzfqdC3O2dpTS4vcUddzBxDbBluAwdaOzp4FqqrkGFm6lsslnR8GWyJr2LBBfme5zdeN5s0DDhwAzp1TXQkFUkuLvmMIgAOCLecN7aWwUB5vvlltHWZ1551AdbUsvCAi8/r8c6C8nGMIfdHmbLdvV1sHBRaDrZ/YsbWfwkJg7Fi55U43WrBANjfn7ghE5vbxx0BQEPClL6muxJwmTgTGj+ecrd20tjLY+oXB1n62b5duLW/d9S42FsjL4zgCkdlt2ABkZwPDh6uuxJxcLs7Z2pE2Y6snBluyjPZ2oLiYYwgD+fKXgU8/BTo7VVdCRL3p6gL+9CeOIQxk3jygtJQjhXbCUQQ/MdjaS2mphFsG2/7deSdw8SKwc6fqSoioN8XFQEMDg+1AbrlF3qDv2KG6EgoUBls/Mdjay/btcgsjM1N1JeY2Z47c3uScLZE5ffIJEBMD5OSorsTcUlOBYcMYbO2EM7Z+YrC1l8JCuRCEhqquxNyCg+Xc+U8/VV0JEfXm00/lCOyQENWVmFtQEJCby2BrJ5yx9RO3+7IPj6dn4RgNbMECGUVoalJdCRFdraVFgtqCBaorsYa8PKCoSK4BZH0Mtn5ix9Y+Dh8G6usZbL21YIHMpnGrHCJzKSyUo69vv111JdaQny/zyNXVqiuhQGhuBqKi9P0etg62UVHs2NqFtkl3Xp7aOqxi2jTZA5LjCETm8umnwKhRwPTpqiuxBm0OuahIbR0UGAy2fmKwtY/t2+U8de756B2XS7q2DLZE5rJxo3RruRe3d+Li5LWfc7b2wGDrJwZb+ygs5BjCYC1YAOzZIyMcRKTexYvArl0cQxgsbc6WrI/B1k9RUTJj292tuhLyx6VLcqZ6fr7qSqxFW5zy2Wdq6yAisXmzXI+4cGxw8vOBffuAxkbVlZA/PB4GW79pP7zWVrV1kH927ZJfCO75ODgJCbIPJMcRiMxh40Zg4kRg8mTVlVhLXp68Idi1S3Ul5I/2dvl7ZLD1g/bD4ziCte3cCQwdCqSkqK7EejhnS2QenK/1TVqaHGjBOVtr07IYg60fGGztwe2W07SCg1VXYj0LFgBHjgA1NaorIXK2+nq5nc4xhMHjQQ32wGAbAAy21ufxSMc2N1d1JdY0f75cFNi1JVJLm3W/7Ta1dVgVD2qwPgbbAGCwtb6TJ4HaWs7X+iouDpg9W26BEpE6GzfKOFVCgupKrCk/Hzh7Vg7rIWtisA0ABlvr27lTHtmx9d2tt8pqbHY6iNT59FOOIfhDuwZwHMG6GGwDgMHW+txuYNw4djn8MX++dL6PHFFdCZEzHTsmnUbuX+u74cPlRMXiYtWVkK8YbAOAwdb6OF/rv4ICmbPdtEl1JUTO9NlnshPC/PmqK7G27GwGWytjsA2AyEh5ZLC1pq4u2beQ87X+iY0FMjNlHIGIjPfpp0BWFo8E91d2NrB7N9DRoboS8gWDbQAEBwMREQy2VlVeLn937Nj6b/58ztkSqeDx9OxfS/6ZMwdoawMOHFBdCfmiuRkIDZV/9GTrYAvIOwMGW2tyu+UW+pw5qiuxvltvBY4f5362REY7eBA4dYrbfAVCVpZcEziOYE1GHKcLMNiSie3cKSfOREerrsT65s2TGT+OIxAZa8sWCWMFBaorsb6oKGD6dAZbq2KwDRAGW+tyuzmGECjDhgEZGVxARmS0LVuk0xgTo7oSe8jOlrUXZD0MtgHCYGtNLS3A/v3yIkaBoe1nS0TG2bIFuOUW1VXYx5w5cjRxW5vqSmiwGGwDhMHWmvbskV0ROF8bOPPny4ztsWOqKyFyhmPH5B8G28DJzgY6O2V3BLIWBtsAYbC1ppISWTmZnq66EvuYN08e2bUlMsbWrfLI+drAmTEDGDKEc7ZWxGAbIAy21rRrl7yAhYWprsQ+RoyQnymDLZExtmyRxU4jR6quxD7CwoCZMzlna0UMtgHCYGtNJSXA7Nmqq7Cf+fO5gIzIKJyv1QdPILMmBtsAYbC1npYWOZyB87WBd+utwJEjwIkTqishsre6OqCqSn7nKLCys4HKSqCxUXUlNBgMtgHCYGs9e/YA3d3s2OpB6x5xHIFIX9p8rTbbToEzZ46c6FZaqroSGgwG2wBhsLUeLhzTT3y8zPxxHIFIX1u2ADfdBCQkqK7EflJTgchIjiNYDYNtgDDYWk9JCReO6Yn72RLpj/O1+gkJkUMvSkpUV0KDwWAbIFqw9XhUV0Le4sIxfd16a8/59UQUeOfPyyECDLb6mTULKCtTXQUNBoNtgERFybwmTymxhtZWWTjGYKsf7WK7bZvaOojsavt2aaYw2OonKwuorgaamlRXQt64fBno6GCwDQjth8hxBGvQThxjsNXPmDEy+8dgS6SPLVuA8eOBSZNUV2Jfs2bJm4c9e1RXQt7QMhiDbQAw2FqLtnBsxgzVldhbQQGDLZFetPlal0t1JfaVliYnkHFnBGvQMlh0tP7fy5Bg297ejqeffhoJCQmIjIxEXl4e/vSnPw345377298iKCio13/q6+u9+t4MttZSUiK7IXDhmL4KCqTTcemS6kqI7KWpSV7HuH+tvrQGCOdsrcHIjm2I/t8C+Pa3v4333nsPK1euxLRp07Bq1Srcfffd+Oyzz3DzzTcP+Oeff/55TJ48+ZqPxcbGevW9GWytpaQEyM1VXYX9FRTI7HlREfDlL6uuhsg+CgtlnIrztfqbNQtwu1VXQd6wVbB1u91455138NOf/hR/8zd/AwB4+OGHkZ6ejqeeegrbt28f8GvcddddmDVrlk/fn8HWOlpbgQMHgO9/X3Ul9peUJOfXb9vGYEsUSFu2yH7RycmqK7G/rCxg1SqgvZ13+czOVjO2a9euRUhICFasWHHlY2FhYXj00UexY8cOnDx5csCv4fF40NjYiK6urkF/fwZb69i/XzodWVmqK7E/lwu4+WbO2RIF2tatctoY52v1N2sW0Nkp1w4yN1sF27KyMiQlJSH6uonh7OxsAMDu3bsH/Bq33XYbYmNjERUVha997Ws4dOiQ19+fwdY6du8GgoK4cMwoBQUyitDRoboSInu4fFlujRcUqK7EGWbMkGsGF5CZn61GEWprazF27NgbPq597FQ/u8RHRUVh+fLluO222xATE4Ndu3bhZz/7GebOnYvS0lKMHz9+wO/PYGsdu3cDKSlARITqSpyhoEDGP8rKgJwc1dUQWV9pqeyZ7sXSEQqAyEg5XpcLyMzPVsG2tbUVYb0Mv4SHh1/593154IEH8MADD1z5/1/96ldx55134pZbbsE//uM/4pVXXhnw+4eEyJYgDLbmt3s3kJmpugrnmDULCA+XcQQGWyL/bd8ub8w5TmWcrCx2bK2guRkIDpY8pjfdg21ERATa29tv+HjbF0eBRQyyPXfzzTcjNzd3wO3CVq5ceWXnBI8HePllYMSIpVi6dOmgvh8Zo6tLtp9atEh1Jc4xZIjsQLFtG/DFuk4i8kNhobxJDA1VXYlzzJoFvPeezNqGGLLPE/li27Y1cLnW4Gtf6/nYxYsXdfleuj8Nxo4d2+u4QW1tLQAgISFh0F9z/PjxqK6u7vdzXnzxxSs7KUyYACxeDDDTmtfhw/KOjh1bYxUUAK+9Jm/+uNiFyHcej3RsH31UdSXOMmuWjFRVVQHTp6uuhvqSlLQU8fFL8dFHPR8rLS3FbB2OGdV98VhWVhaqq6vR2Nh4zcd37twJAMj0IckcOXIE8fHxXn9+VBRHEcxOW0OYkaG2DqcpKADOnAEGsR6TiHpx5Ahw+jTna42mRQjO2Zpbc7Mx87WAAcF28eLF6OrqwmuvvXblY+3t7Vi1ahXy8vIwbtw4AEBdXR0qKyvR2dl55fPOnDlzw9dbv349SktLsXDhQq9rYLA1v927gXHjZP9HMk5+vnRque0XkX+0Ldnz89XW4TSxscDUqZyzNTsjg63uowg5OTl44IEH8MMf/hD19fWYOnUq3njjDRw/fhyrVq268nnPPPMMVq9ejZqaGiQmJgIA5s6di1mzZmH27NmIjY1FaWkpfvOb3yAxMRE/+tGPvK6Bwdb8uHBMjdg2QjSbAAAgAElEQVRYYOZMCbbLl6uuhsi6tm+XW+HDhqmuxHkyM3vu+pE52SrYAsDq1avxk5/8BL/73e/Q0NCAjIwMrFu3DgVXbfbncrngum7I78EHH8Qf//hHfPzxx2hpaUFCQgIee+wxPPvssxxFsJndu4HvfEd1Fc5UUAB88onqKoisbft2jiGokpEB/PznXCtgZrYaRQDkpLEXXngBp06dQmtrK4qKinDHHXdc8zmrVq1CV1fXlW4tADz//PMoLS1FQ0MD2tvbcfToUfzyl78cVKgFGGzN7vRpoLaWHVtVCgqA6mqgvl51JUTW1NAgx4Ez2KqRkQGcPw94cZApKWK7YKsag625abeQuPejGtrFWJsRJKLB2bFDHhls1dAWHe/Zo7YO6huDbYAx2Jrb7t3A0KHA5MmqK3GmCROAxEQuICPy1fbtwOjRwJQpqitxpsREIC6OwdbMGGwDjMHW3HbvlnfcQY54NppTQQGwdavqKoisSZuv5XynGi6XLIJlsDUvBtsAY7A1N+6IoN7NN8s+kP2ccE1EvejoANxujiGolpHBYGtmDLYBxmBrXs3NcmIMg61a+flyJGVJiepKiKxFe0PIYKtWRgZw8CDQ0qK6EuoNg22AMdia1/79skULTxxTa8YM+T0pLFRdCZG1bN8OhIdz8atqM2cC3d1yTSHzYbANsKgo6UZdvqy6Errevn0yW8szvtUKCQFycnpWdxORd7Zvl9+dIUNUV+Js6elyLdm7V3UldL2uLqC9ncE2oLQfJru25rN3LzBtGhARoboSys+XYOvxqK6EyBo8Hh7MYBYREUBSEudszUjLXgy2AcRga1779sltcFIvP18Oyzh6VHUlRNZQUwPU1THYmgUXkJkTg60OoqPlkcHWXDweBlszycuTR44jEHlHO9QkP19tHSQyMuQuIO86mQuDrQ7YsTWnujrg3DkGW7MYOVJu5XEBGZF3duwAUlKA4cNVV0KABNuLF4Fjx1RXQldjsNUBg605aUP+M2eqrYN6aHO2RDSwoqKeOx2kHo/WNScGWx0w2JrTvn3yd8OjdM1j7lx5w9HUpLoSInNraZEAxTEE80hIAEaMYLA1GwZbHTDYmtO+fbLNF4/SNY/8fNmapbhYdSVE5rZrl/yusGNrHjxa15wYbHXAYGtOXDhmPmlpwNChHEcgGkhRkSxM5h7c5pKRIdcWMg8GWx0MGSIb0DPYmkdnJ1BezvlaswkOlg4Ugy1R/4qK5GCG4GDVldDV0tOBQ4fkmGMyh+Zm6aYbtV+9I4ItwGN1zebgQTmJhB1b8+FBDUT983jkd4RjCOaTni5/PxUVqishTXMzEBkp4dYIDLakhHariMHWfPLzZRu2gwdVV0JkTsePy3aFDLbmk5YmjxxHMI/mZuPGEAAGW1Jk3z5gzBjZO5XMhQc1EPVP+91gsDWfoUNlp539+1VXQhoGW50w2JrLvn2crzWruDjpevCgBqLeFRUBU6cC8fGqK6HepKcz2JoJg61OGGzNhTsimBsPaiDqGw9mMDcGW3NhsNVJVBQ3nTeLxkbgyBEGWzObO1cuDJcuqa6EyFza2oDSUh7MYGbp6cCJE0BDg+pKCJDsxWCrA3ZszePAAXlksDWv/HxZWbxzp+pKiMylrAzo6GDH1sy0a4t2rSG12LHVCYOteezbJ6eNpaaqroT6kpwMDBvGcQSi6xUVAeHhXCNgZsnJsnc9xxHMgcFWJwy25rFvH5CUZNxmzTR4QUGy+Tw7tkTX2rEDmDMHCA1VXQn1ZcgQucYw2JoDg61OGGzNgwvHrCE3V4ItD2og6lFUxPlaK0hP5162ZsFgqxMGW3PweIC9exlsrSAvTw5qOHxYdSVE5nDyJPD555yvtYIZM6Rjyzfm6jHY6iQ6msHWDGprgfPnGWytICdHHjmOQCSKiuSRwdb80tPlWlNXp7oSam6WDGYUxwTboUNlmym+e1NLuzXEhRfmN2IEcNNNDLZEmqIiIDERSEhQXQkNJD1dHjmOoF5jo2Qwozgm2EZHA52dQHu76kqcbd8+uSUxaZLqSsgbubk9XSoip+PBDNYxebIsUOYCMrU6OiR3sWOrA+3dAg9pUGvvXnknHeSYZ5615eUBu3fLpvRETnb5MrBrF4OtVQQHA9OnM9iqpmUudmx1oL1baGxUW4fTcUcEa8nNlXfcu3erroRIrb175Q0ed0SwDh6tq56Wudix1QE7tup1dQGVlT2zT2R+GRlAWBjnbIl27JD9UbOyVFdC3kpPl9PHurtVV+Jc7NjqiB1b9Y4elY7H9OmqKyFvaRdyBltyuqIi+V0IC1NdCXkrPR1oaZFrD6nBjq2O2LFVTzu3Oy1NbR00OHl5XEBGxIMZrEcbe+M4gjrs2OqIHVv1ysuBuDhg7FjVldBg5OZKx+PMGdWVEKlRXw8cOcKFY1YzdiwwbBiDrUpa5mKw1YH2Q2WwVefAAenWulyqK6HByM2VR44jkFPxYAZrcrl4tK5qWseWowg6CA2V2SiOIqhTXs75WiuaNAmIj2ewJecqKpLuX2Ki6kposLgzglqNjbL1Wni4cd/TMcEWkHcM7Niq0dUFVFRwvtaKXC7O2ZKz7dwpR0zzbpP1zJgBVFXJPsRkvKYmyV5G/u44KtgOHcqOrSo1NdwRwcpycwG3m9vmkPN0d8vBDDk5qishX6Sny6mj1dWqK3Emo4/TBRwWbNmxVYc7Ilhbbi5w6ZJ0PoicpLpanvsMttak7ZvOOVs1GhuNna8FHBZs2bFV58ABIDYWSEhQXQn5IjtbbiVxzpacxu2Wxzlz1NZBvhk2TOajy8tVV+JMTU3s2OqKHVt1ysu5I4KVxcYCqakMtuQ8xcVAUpJsVUjWlJbGYKsKRxF0xo6tOgcOcL7W6nJzuYCMnMft5hiC1THYqqMtHjOSo4ItO7ZqcEcEe8jNlTm1lhbVlRAZ4/JlYPduBlurS0sDDh7kzggqsGOrs6FDGWxV4I4I9pCbK29SSkpUV0JkjL17JQxlZ6uuhPyRliavXYcOqa7Eedix1Vl0NEcRVNBuATHYWlt6OhAZyTlbcg63GwgJATIzVVdC/khNlUeOIxiPHVudsWOrxoEDQEwMd0SwupAQWRnOOVtyCrcbyMgw9tQkCrz4eGDkSAZbFdix1RkXj6mhHaXLHRGsLzeXHVtyjuJijiHYBReQqcGOrc6io4HWVjmFhIxz4AAXjtlFbi5w4gRw6pTqSoj0demSLHrlwjF7SEuTv08yTnc3O7a60941NDerrcNJurvlxYTztfaQmyuP7NqS3ZWUAB4Pg61dpKXJyYlsbBlH20GHHVsdae8aOGdrnJoa6ZKzY2sP48cD48Yx2JL9FRcDUVFASorqSigQUlOB9nbg6FHVlTiHlrUYbHWk/XAZbI1z4IA8smNrHzyogZzA7ZbFksHBqiuhQNCaK5yzNY62pomjCDrSfrhcQGac8nLZEWHcONWVUKDk5Mht2q4u1ZUQ6YcnjtnL2LFyNDiDrXHYsTUAO7bG0xaOcUcE+8jOljeHVVWqKyHSR10d8PnnDLZ24nJxAZnR2LE1ADu2xisv53yt3cyeLRcJt1t1JUT6KC6WR271ZS/c8stY7NgagB1bY3FHBHuKjZUFNdrFn8hu3G5g1CggMVF1JRRIqalyTeruVl2JM7Bja4CICCAoiB1bo9TUyHYfDLb2k53Nji3ZlzZfyxEqe0lLk2vS8eOqK3EGrYnIYKsjl0t+wOzYGkO75cNRBPvJyQH27JHtc4jsxOPhiWN2xZ0RjNXUJFvmBRmcNB0VbAEZR2CwNUZ5ufy8x49XXQkFWnY20NEh4ZbITg4fBhoauHDMjiZMkKDFBWTGaGw0vlsLODDYRkdzFMEoFRUy08TbefaTkQGEhnIcgexHe06zY2s/QUFyTWLH1hiNjcYvHAMcGGzZsTVORQVP7bGrsDAgM5PBluynuBiYMgUYMUJ1JaQH7oxgnKYmdmwNwY6tMTyeno4t2VN2NndGIPvhwQz2pnVsPR7VldgfO7YGYcfWGHV1wKVLDLZ2lpMDVFYCFy+qroQoMDo6gNJSBls7S0uTa9OpU6orsT92bA3Cjq0xtOF8jiLYl3bxLylRWwdRoBw4ALS1cb7WzrSdEbiATH/s2BqEHVtjVFbK4qIpU1RXQnpJTpbfJ87Zkl243UBwMJCVpboS0svkybJGgHO2+mtqYrA1BPexNUZFBXDTTRJuyZ6CgoA5cxhsyT7cbiA9XbaEInsKDpY7iQy2+uN2XwYZOpSjCEbgwjFn4AIyshMezOAM3PLLGOzYGoSjCMaorOR8rRPk5AAnTgC1taorIfJPczOwfz8XjjkBt/wyBju2BtEWj3GrD/1cugScPMmOrRNoIYBdW7K60lKgu5vB1gnS0oBz54D6etWV2JfHw8Vjhhk6VH7gLS2qK7Gvqip5ZLC1v/HjgdGjOWdL1ldcDEREANOnq66E9KbdTdSuVRR4HR1AZyc7tobQfsics9WPto1KcrLaOkh/Lpd0uBhsyercbmDWLCAkRHUlpLebbpLFr5WVqiuxr+ZmeWTH1gDaD5lztvqpqAAmTFDzTo2Ml5Mj3S6O95CV8cQx5wgLk60oGWz109oqjwy2BtDCFoOtfrhwzFmys4ELF4BDh1RXQuSbs2eBo0cZbJ0kOZmjCHrSOrYcRTCA9u6Bowj64VZfzqJtj8RxBLIqbfEjt/pyjpQUdmz1xI6tgdix1dfly9K5Y7B1juHDgalTuTMCWZfbLc9jnpToHCkp0qVva1NdiT2xY2sgdmz1dfgw0NXFUQSn4QIysjJtvtblUl0JGSUlRbZ34wiVPtixNRA7tvrSdkRgx9ZZcnKAsjLZ4oXISjwenjjmRFrzheMI+mDH1kDBwbJXITu2+qisBOLigFGjVFdCRsrOllt6+/erroRocI4dA86c4cIxpxk5EhgxgsFWLy0twJAh8o/RHBdsAR6rqydt4Rhv6TlLVpa8aeQ4AlmN9pxlx9Z5uIBMPy0t6rb8dGSwjY5msNVLRQXna50oMhKYMYMLyMh6iouBxEQ5QY+chcFWPy0tauZrAYcG26FDOYqgB49HXiQ4X+tM2dns2JL18GAG59L2suXhMoHHYGswdmz1ceKEDIwz2DpTTg5w4EDPogEis+vqAkpKGGydKiVFmlynTqmuxH6amzmKYCh2bPWh3dLhKIIzZWfL9jmlpaorIfJORYVcgDlf60zcGUE/ra3s2BqKHVt9VFTICsjJk1VXQipMny47jnAcgazC7ZaFrrNnq66EVJg8GQgNZbDVAzu2BmPHVh8VFUBSkqyOJ+cJCZGAwAVkZBVuN5CWpq6zRGqFhADTpjHY6oEdW4Nxuy99cOEYcQEZWUlxMedrnY47I+iDHVuDcRRBH9zqi3Jy5Pz1M2dUV0LUv9ZWYO9eztc6HYOtPrgrgsE4ihB4DQ3A6dPs2Dqd1v3atUttHUQD2b0b6Oxkx9bpUlJkRx82uwKLwdZg7NgGXlWVPLJj62yTJ8sxlRxHILMrLgbCwuRgEXKu5GR5rK5WW4fd8OQxg8XEAB0dQHu76krsQwu2SUlq6yC1XC65tcsFZGR2bjeQmanmLHsyDy3YatcwCoy2dnZsDRUTI48tLWrrsJOqKmD8eCAqSnUlpJq2gIyn+ZCZ8cQxAoDYWGDsWM7Z6kHLWkZzdLDlnG3gVFX1vPMlZ8vJkcVjx46proSodw0NwMGDDLYkuIBMHwy2BoqNlUcG28BhsCWNtsqc4whkVtriRu6IQACDrV4YbA3Ejm1gdXUBhw4x2JIYPRpITOQCMjIvt1saHNOmqa6EzCAlRRaPdXWprsReGGwNpHVsm5vV1mEXtbWyEI/BljQ5OQy2ZF7FxdKtDXLkFZCul5Ii1zCOTwUWg62B2LENLO3FgMGWNDk5QEkJOyBkPh4PsHMnxxCoh3bt4jhCYDHYGig8XLZ4Ycc2MGpq5GeamKi6EjKL7Gz5/aqoUF0J0bVOngTq6rhwjHpMmABERDDYBhr3sTVYTAw7toFy7JjMqvG2Hmlmz5Y9bbmAjMxGG5FhsCVNUJB0bRlsAycqUl0mcGwUiY1lsA2UY8c4hkDXGjpUjlfmnC2ZTXExkJAg/xBpUlJ4SEMgqdzT3rHBNiaGowiBUlPDYEs34gIyMiMezEC94ZZfgcVgqwBHEQLnzFkGW7pRdjawdy/Q1qa6EiLR3S172DLY0vVSUoD6euDiRdWV2IOq+VrAwcE2NpYd20BisKXr5eQAnZ3A7t2qKyESx44Bly4x2NKNUlLkkVt+BQY7tgqwYxtYDLZ0vZkzZfcRLiAjszhwQB5nz1ZbB5nPtGmy4LWmRnUl9sBgqwAXjwXOiOE9h14QaYYMATIzOWdL5rH/gLwJj4tTXQmZTWSkbFl59KjqSuyBwVYBdmwDZ+JE1RWQWeXksGNL5lF+gGMI1LeUFHZsA8XWM7bt7e14+umnkZCQgMjISOTl5eFPf/qTV3/2woULWLFiBeLj4xEdHY3bb78dZWVlAamLM7aBM2mS6grIrLKzZQudxkbVlRDJc5EnjlFfGGwDx9Yd229/+9t48cUX8fDDD+Oll15CcHAw7r77bmzfvr3fP9fd3Y177rkHa9aswRNPPIEXXngB9fX1mD9/Pg4dOuR3Xdzuy3/d3fLIji31ReuO8QQyMoOOTnZsqW8pKcCJE6qrsAfbBlu324133nkH//zP/4x/+Zd/wXe/+11s3LgREydOxFNPPdXvn127di127NiBN954Az/5yU/w/e9/H5s2bUJwcDCeffZZv2uLjQW6uv3+Mo5WXy+PDLbUl6QkeRO5f7/qSoiAkBAgI0N1FWRWKSnMBf7yeOQxyq6jCGvXrkVISAhWrFhx5WNhYWF49NFHsWPHDpw8ebLfPztmzBjcd999Vz42cuRILFmyBB9++CE6Ojr8qi0mxq8/TujZFoWjCNSXoCBgzpye1ehEKk2bBoSHq66CzIq7+/ivtVUeo+3asS0rK0NSUhKir5sizv5iyGl3PxtclpWVYdasWTd8PDs7Gy0tLaiurvarNq7i91/NF8GWR1NSf3JyGGzJHNKnq66AzGzMGCAqUnUV1qaNeEYq/DnqGmxra2sxduzYGz6ufezUqVO6/FlvsGPrv2M18hgSorQMMrnsbKD+jOoqyMm0HXCmM9hSP1wuIJGjdX7RftdUztjqGklaW1sRFhZ2w8fDv7gX1Kr1rHvR1tbm858FgIoBVqvIFETFlc/t/6tRbw6U8+dHA4uIAPi7Riod3VCB+wFERFSgtFR1NWRmw+L4WuWP2vIKTAZw5szAv2sD5TRf6RpsIyIi0N7efsPH2744PD5CrngB/7MAsGzZsgHry/ri8aFlyxCYTcSchT8/8hafK6RSFoD7ATz9zDKUPaO6GjIzvlb5JwvAPQB++KNlKPuRmhp0DbZjx47tdWSgtrYWAJDQz3CmP38WAN58802kpqb2+e87O4E/y60AsAxvvfkmWvv5XLpRWxvwlzfz50feefm7FUAZnyukxmt/VgEU8/lHA9v9mwrgV8vw2q/fRNAcPlcGa//qCuDfl+HVV95ESE7/P7+KigqvmpCDpWuwzcrKwqZNm9DY2IihQ4de+fjOnTsBAJmZmX3+2czMTGzduhUejwcul+uaPxsVFYWkpKR+v3dqamqvi8+uFhEOoE0+FwN8Ll1r796e/82fHw0kPx9AGZCcnIogPlfIYMePyyNfq2ggkZUAfgWEhaViBp8rg3byD/KYlZWKUEU/P10Xjy1evBhdXV147bXXrnysvb0dq1atQl5eHsaNGwcAqKurQ2VlJTo7O6/5s6dPn8b7779/5WNnz57Fu+++i3vvvRehoaF+16dyuNnqqqpUV0BWkpYmj59/rrYOcp7aWqDutOoqyCoSE+VR286SBkfbFSEAEc1nunZsc3Jy8MADD+CHP/wh6uvrMXXqVLzxxhs4fvw4Vq1adeXznnnmGaxevRo1NTVI/OJZtXjxYuTl5WH58uUoLy/HiBEj8PLLL8Pj8eC5554LSH3R0QDOBeRLOU5lJRAbA+CS6krICrRge+AAMHGR2lrIWYqLVVdAVqJtU8Vg6xsznOiq+0ZNq1evxk9+8hP87ne/Q0NDAzIyMrBu3ToUFBRc+RyXy3XNuAEABAUFYf369fjBD36Al156Ca2trcjJycHq1asxbdq0gNTGjq3vqqq+OHFsn+pKyAq0faMPHADuVlsKOUxxMTBiOIDzqishK2Gw9Y223ZdKuo4iAHLS2AsvvIBTp06htbUVRUVFuOOOO675nFWrVqGrq+tKt1YTFxeH119/HWfOnEFTUxM2btw44NzsYEQrPPLN6qqqeOIYDR4PaiCjud3cv5YGj8HWN41OCLZmxo6tbzyeqzq2RINQVQX4eRo2kdc8HunYMtjSYB0/DnR3q67CepoaVVfg8GDLjq1v6uqAxkYGWxq89svA/v2qqyCnOHwYaGhgsKXBa7/Mxa6+cMQogpkx2PpG2xGBowg0WMFBcmuYyAjac01bvEg0GNXVqiuwHgZbxRhsfVNVBQQFAePHq66ErOammxhsyThuNzB1KhAXp7oSspqQEG5r6QsGW8U4Y+ubqipg8mRgyBDVlZDVTE/n9ktknOJiICdHdRVkRRPGM9j6gsFWMS3YckB8cKqqgORk1VWQFU1Pk50RzLDXIdlbRwdQWgpkZ6uuhKxo0iSOIviCwVYxbRSBF9nBYbAlX6WnyxvJ0lLVlZDd7d8PtLUx2JJvEhPZsR2sri6gpVV1FQy2ABhsB6O9HTh6lMGWfDN5spzswzlb0pvbDQQHA4qOqyeLmzRJtvxqNUFQs4pLJjmJlMEW5midW8Xhw9JxY7AlX4SESNDgnC3pze0GZszoOSKVaDASE2Uf5EOHVFdiHRcvqq5AODrYajO27Nh6T7s1w2BLvsrJYceW9Od2c+EY+U7bzpJztt5jsDUBdmwHr6oKiIkBxoxRXQlZVXa2jLOcOaO6ErKrxkZZpMhgS76KiwOGDeOc7WAw2JoAO7aDpy0cc7lUV0JWpYWNXbvU1kH2VVoqt5EZbMlXLheQlMSO7WAw2JqANnvFjq33uCMC+WvyZGDECI4jkH7cbmlc8MQx8kdyMju2g8FgawJBX/zXM9h6j8GW/OVyyTgCF5CRXtxuYPZs2RWByFdJSXLN83hUV2INFy8CISb4nXN0sNVwFME7Z88C588z2JL/tAVkvGCQHrhwjAIhORloaADOnVNdiTVcvNizdkklBluwY+st7ohAgZKdLYvHjh9XXQnZTV2dPK9yc1VXQlaXlCSPHEfwDoOtibBj652qKrmNPG2a6krI6rTToDhnS4GmjbiwY0v+mjZNrnlcQOYdBlsTYcfWO1VVsml1RITqSsjqRo+W5xKDLQWa2y3PrwkTVFdCVhcRwaN1B4PB1kQYbL3DhWMUSDk5XEBGgafN13JLQgoEbvnlPQZbE2Gw9Q6DLQVSTo7sZdvVpboSsguPhwvHKLC45Zf3GGxNhDO2A+vsBA4fZrClwMnOlt+9ykrVlZBdHDoEXLjAYEuBk5Qkzyu+AR8Yg62JMNgOrKYG6OjoWSVK5K/Zs+V2MedsKVC059KcOWrrIPtITgYuXwaOHVNdifldvAgMHaq6CgZbABxF8IY2Y8SOLQXK0KFAairnbClwdu6UlezDh6uuhOxCu+ZxHGFg7NiaSFu7dCOpb1VVskJ0/HjVlZCdaAc1EAUC52sp0CZMAMLDuYBsIF1dQGMjg62pXLqkugJzq6qSTkgQnzEUQDk5wJ49QFub6krI6i5fBsrKGGwpsIKC5NrHjm3/GhvlkcHWRC5eVF2BuVVXcwyBAi87WxYm7tmjuhKyur17Jdwy2FKgccuvgWkZisHWRC5cUF2BuVVVceEYBd7MmcCQIRxHIP+53UBICJCZqboSshtu+TUwLUPFxKitA2CwvYLBtm9NTcCpU+zYUuANGSJBhAvIyF9uN5CRIfOQRIGUlAScOMEdlPqjZSjuimAiDLZ9027BsGNLeuACMgoELhwjvWhNnYMH1dZhZgy2JtTQoLoC89JuwbBjS3rIzpbnGOfcyVcXL8pBHwy2pAetqcNxhL5pwZYztiYRFcmObX+qq4FRo4C4ONWVkB1pYWTXLrV1kHWVlMhxugy2pIfhw4GRI7mArD8NDUBkJBAaqroSBlsA0jpnsO0bF46RnpKSZMEBxxHIV263vI7zrhLphQvI+nfhgnmaXwy2YLAdSFUVLxikn6AgOQKVC8jIV263PIeCg1VXQnbFLb/6d+ECMGyY6ioEgy0YbPvj8cgvMzu2pCcuICN/cOEY6U3r2Ho8qisxJ3ZsTWboUC4e60ttrWz3xY4t6Sk7Gzh5UraVIxqMkyflHwZb0lNyspxQevq06krMicHWZNix7Zt264XBlvSkhRKOI9Bgac+Z3Fy1dZC9aXctOY7QOwZbk2Gw7VtVlcytTZmiuhKys3HjgLFjgZ07VVdCVuN2AwkJ8hwi0svUqbIegAvIesdgazIxMQy2famqAiZPlhOiiPTicknHjcGWBovztWSEsDBg0iR2bPvS0MDFY6YSHc1g2xcuHCOj5OXJbeWuLtWVkFV0d8tzhsGWjMAtv/rGjq3JDB0qZ0B3dKiuxHy41RcZJTcXaGwEKipUV0JWUVUlC3oYbMkI3PKrd11d8nvIYGsi2tnG7Npe6/Jl4OhRBlsyxpw5MsPGcQTylrZF3Jw5ausgZ0hOBg4fZhPsepcuySODrYkw2PbuyBF5J8ZRBDJCdDSQng4UFamuhKzC7QZSUoDYWNWVkBMkJwOdndLwoR5admKwNREG295ps0Ts2JJRuICMBoMLx8hI3PKrdwy2JhQTI48MtteqrpYu2tixqishp8jNBQ4ckFlbov60tQF79jDYknHGjQMiI7mA7HpaduKuCCYSHS2PDLbXqqqSd6gul+pKyCny8mSl+65dqmdt5X0AACAASURBVCshsysrk1nHvDzVlZBTuFxcQNYb7eRWdmxNJCpKnrA8Vvda1dUcQyBjpaTIaBDHEWggRUVAeDgwc6bqSshJuOXXjbSmoHb3WzUGW8hK7NhYdmyvp3VsiYwSHCy3lhlsaSBFRbIbQmio6krISZKT2bG93oUL0pAICVFdiWCw/UJcHIPt1S5cAOrr2bEl4+XmSmjxeFRXQmZWVCTPFSIjJSUBtbU9W1yRuQ5nABhsr2CwvZb2jpTBloyWmwvU1QGff666EjKrU6eA48c5X0vG066J7Nr2YLA1qWHDOGN7NW2GaNo0tXWQ82hdOO5nS33RRlUYbMlo3PLrRg0NDLamxGB7repqICGhZ49fIqOMHg1MmsQ5W+pbUZFsvTR+vOpKyGliYoAxY7iA7GoNDcDw4aqr6MFg+wUG22tx4RipxIMaqD9FRezWkjrc8utaDQ3m2cMWYLC9Yvhw4Px51VWYR1UV52tJnbw8oKSEZ7LTjTo7ZZ9jBltShVt+Xev8eXZsTYkd2x7d3cDBgwy2pE5urpwstXev6krIbPbvB1paGGxJHW3LL+7cItixNanhw+Uvp7tbdSXqnTgBtLZyFIHUycqS/Uk5jkDXKyqS/TJnzVJdCTlVUhLQ3Cy7czidx8OOrWkNGyahlmfUc6svUi88HMjM5M4IdKOiIjltLDJSdSXkVNq1keMIcveko4MdW1PS3m1wzlZ+WUNDZWU6kSpcQEa94cIxUm3yZLlrwAVkPZmJwdaEtL8UztlKsJ061TzH45Ez5eXJhYNvNklz/ry8PjHYkkqhocCUKezYAj2ZiaMIJsSObY/qao4hkHraQQ1ut9o6yDy05wKDLammLSBzOnZsTYwd2x7cw5bMYOpUYMQIjiNQj6IiaULcdJPqSsjpkpLYsQXYsTW1mBggKIgd27Y24NgxdmxJPZdLurZcQEYabb7W5VJdCTldcjJw9Chw+bLqStTSMhOP1DWhoCD5i3F6x/bQIdm+gx1bMgNtARn3i6TubnkucAyBzCApSZ6Thw6prkSthgYgNhYIDlZdSQ8G26vw9LGeWyvs2JIZ5ObKC+fBg6orIdUOHgQuXGCwJXNISZFHp48jnD9vrvlagMH2Gjx9TIbh4+KA+HjVlRABOTnyyDlb0kZSsrPV1kEEAKNGSafS6cG2ocFc87UAg+012LHtWTjGGTYyg2HD5O4B52ypqAhITTXXLB85l8slr01OD7bs2JocO7bc6ovMJz8f2LFDdRWkGg9mILNhsGXH1vTYseVWX2Q+c+cCe/YATU2qKyFVmpuBvXsZbMlcUlKAykpnL25lx9bknN6xPXtWnqTs2JKZzJ0rq4+Li1VXQqrs2iXPAQZbMpPkZMkMZ8+qrkSdhgYGW1NzesdWO0WFwZbMJDVVFmkUFqquhFQpKgKiooDp01VXQtRDu1Y6eRzh/HmOIpjasGFyu7OjQ3Ulami/nDzVh8wkKEg6dQy2zlVUJDtkmGmvTKKbbpJFZE4Ntl1dwMWL7Niamvauw6njCFVVQGIiEBmpuhKia82dKwvIurtVV0JG83gk2Obmqq6E6Frh4cCkSTJn60QXL8rvJzu2Jqa963BqsK2u5sIxMqe5c+X30qmdESc7fhyoq+N8LZlTSopzX5e0rMSOrYlp7zrOnVNbhypVVZyvJXPKyZGRBG775TzaCEp+vto6iHrj5C2/tKzEjq2JjRghj04Mtl1dcuY1gy2ZUUwMMGMG52ydqLBQZhlHjVJdCdGNkpOBI0ecuTZHy0padjILBturODnYHjsGXL7MUQQyr/x8BlsnKiyUURQiM0pOBjo7gcOHVVdiPAZbCxgyBIiOduaWX9qtFHZsyazmzgUqKpz5++lUTU1yOAeDLZlVSoo8OnEc4dw5WUBntgXnDLbXGTHCmR3b6mogLAyYMEF1JUS908JNUZHaOsg4xcUyJsVgS2Y1ZgwwdKhzg63ZurUAg+0NnBpsq6qAadO4TySZ15QpMmfJBWTOUVgo89U8mIHMyuVy7gIyBluLcGqwra7mGAKZm8slnTvO2TpHYaHMVgfxSkUmlpzszL1sGWwtwqnBtqqKC8fI/PLzgZ07ZbEG2Vt3NxeOkTU4dS9bBluLcGKwbW4GTpxgx5bMb+5ceb7u26e6EtJbZSVw4QKDLZlfcrLkBqdlBwZbi3BisD14UB7ZsSWzmz0bCA3lnK0TFBbKCEJOjupKiPqnNYWc1rVlsLUIJwZbbTaIHVsyu4gIYNYsztk6QWGhHMoRE6O6EqL+TZsmawCcNmfLYGsRI0YAbW1AS4vqSoxTWSmrzc12LB5Rb7iAzBkKC4Gbb1ZdBdHAIiKAiROd1bFtb5exMAZbC3Di6WOVlT2bTBOZXX4+cPQoUFuruhLSy9mzEhI4X0tW4bQtv8x66hjAYHsDJwbbqioGW7KO/Hx55JytfWmHcDDYklUw2JoHg+11nBZsu7sZbMlaxo8HEhMZbO2ssFBOdJo0SXUlRN5JTgYOHwY6OlRXYgwGWwtxWrD9/HOgtZXBlqyFc7b2tn27/B27XKorIfJOSoqE2qNHVVdiDAZbC4mJAUJCnBNstVWcDLZkJXPnArt2yQIGspeODsDt5hgCWYvTtvw6d07eeMbFqa7kRgy213G5ZHcAJwXb8HC5tUtkFXPnApcvA6WlqiuhQNu9W3am4Y4IZCUJCUB0tLOC7bBhQHCw6kpuxGDbCyftZVtZKQczmPHJSdSXmTNlix2OI9hPYSEQFgZkZamuhMh7LpdcS50UbM04hgAw2PbKacGWBzOQ1YSGyolUDLb2U1gIzJkj4ZbISlJSnHNIA4OtxTgt2HK+lqxo7lxZZOTxqK6EAsXjAbZt43wtWZOTtvxisLWYkSNlg3C7u3gRqKtjsCVrmjcPOH0aOHRIdSUUKEePAqdOyd8tkdUkJwNnzgANDaor0R+DrcU4Jdhq7ywZbMmKtO2gtm5VXQkFyrZt8siFY2RFTtoZ4cwZID5edRW9Y7DtRXy8/KXZnTYLlJSktg4iX8TGAhkZPWGIrG/rViA9XXamIbIa7VrqhDlbBluLGTkSaGy0/x6ZlZXAhAmyRQmRFRUUsGNrJ1u3yt8pkRVFRsrWmXbv2HZ0ABcuSFYyIwbbXmjvQuw+jsCFY2R18+bJjG1dnepKyF/19RIIOF9LVuaEBWTa4np2bC1E+8uy+zgCgy1ZnRaC2LW1vu3b5ZHBlqzMCcFWy0YMthbihGDb0SGdLgZbsrKxY4GpUxls7WDrVmDiRBmPIrKqlBTg4EGgs1N1JfphsLUgbW7EzqMIR49KuGWwJasrKOACMjvgfC3ZQXKyXFtralRXoh8tG3HG1kKiooDwcHt3bLVVmzx1jKxu3jxgzx7g0iXVlZCvmpqAsjKOIZD1addUO++McOaMnP4YG6u6kt4x2PbC5bL/ll9VVbIbQkKC6kqI/DNvHtDdzeN1rayoCOjqYrAl6xs/Xq6tdg+2I0dKVjIjBts+2P2QBm3hmFmfmETemjYNGDWKc7ZWtnWrnGKUmqq6EiL/uFxybS0vV12Jfs6eNe8YAsBg2ye7d2y5IwLZhcslnT4GW+vS5mv5RpvsIDUVqKhQXYV+zHw4A8Bg2yc7B1uPR37pGGzJLgoKALfb/oeq2NHlyzKKwIVjZBdasPV4VFeiD8cH2wsXLmDFihWIj49HdHQ0br/9dpSVlXn1Z//u7/4OQUFBN/wTERGhc9XSZrdrsD17FmhoYLAl+5g3T0Ltrl2qK6HBKisDWls5X0v2kZoKXLxo34NjtBlbswrR84t3d3fjnnvuwd69e/HUU09hxIgRePnllzF//nyUlJTgpptu8urrvPrqq4i+6tzX4OBgvUq+Ij7evjO22lA7gy3ZRUaGLNjYuhW4+WbV1dBgbN0qR5HOmqW6EqLASEuTx4oK2Wvbbs6eNXfHVtdgu3btWuzYsQNr167FfffdBwBYsmQJkpKS8Oyzz+Ktt97y6ussXrwYw4cP17PUG8THy7Fx3d1AkM0GNior5b/Jy/cVRKYXEgLMnSsh6ZlnVFdDg7F1K5CXJ9sHEdnBlCnAkCGygOz221VXE1gej/mDra6Rbe3atRgzZsyVUAsAI0eOxJIlS/Dhhx+io6PDq6/T3d2NS5cuwWPgwEp8vITa8+cN+5aGqayUX7ywMNWVEAXOvHlyLGtXl+pKyFvd3XK4BscQyE5CQmS3FjsuILtwQU5Vc2ywLSsrw6xe7i9lZ2ejpaUF1dXVXn2dKVOmIC4uDjExMXj44YdRX18f6FJvYOfTx6qqOIZA9lNQIHNtBw6oroS8VVkpzQMuHCO7sevOCGY/dQzQOdjW1tZibC8DJtrHTp061e+fHz58OB5//HG89tpreO+99/Dd734X77zzDubNm4fGxkZdatZo70bsuICsooInjpH95ObK7ewtW1RXQt7auhUIDpZRBCI7sWuw1TKRmTu2Xs/YejwetHu5l054eDgAoK2tDWG93O/W/n1ra2u/X+eJJ5645v8vWrQIOTk5eOihh/Dyyy/j6aef9qoeX2h/aQY0hw3V0gIcPdoz3E5kFxERQE4OsHkz8Jd/qboa8samTcCcObLwj8hOUlNlV4SGBmDYMNXVBI6tgu3mzZtxu5dT0JWVlUhKSkJERESvYbitrQ0AfNq2a+nSpXjyySfx6aef9htsV65cidjrDjJeunQpli5d6tX3GTZM5mTsFmyrqmT4m8GW7Gj+fODXv5bnODf7NzePR4Ltt76luhKiwLt6Z4S5c9XWEkinT8tr62BHEdasWYM1a9Zc87GLFy8GsLIeXgfb1NRU/Pa3v/Xqc8eMGQNARg56Gzeora0FACQkJHj77a8xfvx4nB9gVdeLL77Y63yvt4KC5B3J6dM+fwlT0o7549GVZEe33Qb84z/K83z6dNXVUH+qq6WjddttqishCrykJAmAdgu29fUSage762pvjcXS0lLMnj07gNUJr4Pt6NGj8cgjjwzqi2dmZmLr1q3weDxwXdU+2blzJ6KiopCUlDSorwfISERNTY0uP4zrjR5tv45teTkwbhxwXTObyBby82XOdtMmBluz27RJLo7cd5jsKCICmDzZfnO2p09LNjIzXRePLV68GKdPn8b7779/5WNnz57Fu+++i3vvvRehV21cePz4cVRqJwd84UwvK7deeeUVnD17FgsXLtSv8C+MHm3Pji3HEMiuIiNlEdlnn6muhAby2WdAdjbna8m+7LiAzArBVtcDGhYvXoy8vDwsX74c5eXlV04e83g8eO6556753EceeQRbtmxBd3f3lY9NnDgRDz74INLT0xEeHo5t27bhnXfeQVZWFh577DE9SwcAjBoFHDmi+7cxVHk5cNddqqsg0s/8+cCrr9rzcBW70OZrly9XXQmRflJTgffeU11FYNXXAz5OkRpG15f9oKAgrF+/Ht/4xjfw0ksv4amnnsKoUaOwceNGTJs27ZrPdblc14wrAMCyZcvgdrvx3HPPYeXKlSgpKcHTTz+NLVu2XNlZQU92G0VobwcOHWLHluxt/nzZa1GbJyfzqaqSzs/8+aorIdJPWhpQUyO7EdmF4zu2ABAXF4fXX38dr7/+er+f91kv9w5fe+01vcryit1GEaqrpYvFYEt2lp8vx1lu2gSkp6uuhnqzaZPsOsP5WrKz1FS5O1FVBWRlqa4mMKwQbHmjrh+jRgGXLgFf7E5medwRgZxAm7PdtEl1JdSXTZs4X0v2p11r7TJne/my7Ms7apTqSvrHYNsP7V2JXcYRysvlv2nECNWVEOlr/nwJT1eN7JNJaPO1HEMgu4uNBcaOtU+w1dbzs2NrYdpfnl3GEbgjAjnF/PnAuXPAgQOqK6HrVVZyvpacw047I2hNPgZbC9Pa7Qy2RNZy9ZwtmYs2X2unTeuJ+mKnYKtlIY4iWJh2FrIdRhE6OmTxGIMtOUFEBJCXx2BrRps2ATk5nK8lZ0hLk2tvR4fqSvzHYGsDoaHA8OH26NgeOgR0djLYknPMnw9s3sw5WzPhfC05TWqqXHsPH1Zdif/q64GYGMCA3Vb9wmA7ALts+aXtiMBgS06hzdnu36+6EtJUVMjFkcGWnMJOOyNYYasvgMF2QHY5pKG8XHZD0MYriOwuL49ztmbD+VpymtGjgbg4ewTb+noGW1sYNco+Hdu0NOC6w92IbItztuajzddGRamuhMgYLpd9FpCdPm3++VqAwXZAdhpF4BgC/f/27j2uqnLNA/hvb1ERRBAtwSuJSobgBVTyhngZxdLU1DJPHrPLzOSnTk5anbKyyc6Z8lTnnCnr08ykdpzjocQuljZeEzWHQYREE0zzEgiKYgYqoLLmj2c2xaCyL2vtd621f9/Phw+1Ya/1CC9rP/tdz/u8gYZ1tubB+loKVL1722OLb5Yi2ERUFFBWpjoK31y5Ilv6MbGlQJOWBlRUAN98ozoSOnBAGrynpamOhMi/brtN+jdb/Q12WZnkRGbHxLYJ0dGyAKW2VnUk3jt6FKipYWJLgef222WL3c2bVUdCmzYBLVsCQ4eqjoTIv+LjgYsXgePHVUfivStXpMY2Olp1JE1jYtsE1y/RyrO27IhAgaplS2DECCa2ZrBpEzB8uNQ+EwWSPn3ks5U7tJw+LeVETGxtwPVLLC1VG4cvvv325z2riQLNmDFAVhZQXa06ksBVWyu1zmPGqI6EyP86dZL+r1be4tuVA1khj2Bi2wS7JLbsiECBauxYSWq//lp1JIFr9265FTt2rOpIiPzP4ZBZWyvP2DKxtZH27aXvoh0SW6JA1KePtKjZtEl1JIFr82bpo92vn+pIiNSIj7f+jK3DwXZftuB0SnsLq9bY1tVJ/zwmthSonE65Bc46W3U2bQJGj5bfBVEg6tNHXouvXlUdiXdKSyWpDQpSHUnTeJlxQ3S0dWdsjx8HLl1iYkuBbexYIDdXOpyQf/34I5CTwzIECmzx8dKd6MgR1ZF4p7TUGmUIABNbt1g5sWVHBCKZsdU0YNs21ZEEnm3b5M4RF45RILN6ZwQmtjYTFWXtxDY0FOjSRXUkROp07gzceivrbFXYvBno0QOIiVEdCZE6N98sdeZWrbMtLbXG5gwAE1u3WHnGdv9+uQXCjggU6Fhnq8amTZytJbJ6ZwTO2NpMdLTskWzFou+CAiAhQXUUROqNHQt8/718kH8cPw589x3ra4kAmWSyYmKrabKAnomtjURHS1J75ozqSDxz5YqUIjCxJQJSU4FmzThr60+bN0snhLQ01ZEQqdenD3DokGxYYiVnzwKXLzOxtRWrbtJw+LCswmRiSyS77w0ezDpbf9q0CUhOBtq2VR0JkXrx8TLhdOiQ6kg8Y6XNGQAmtm6xamJbUCCfXasxiQLdmDHA1q3WLCuymro6YMsW1tcSucTHy2erLSBjYmtDrpWAVkts9++XlZhW2CmEyB/GjgUqKoC8PNWR2N8330j5FutriUS7dpIcWq3O1pX7sCuCjTRvLsnhyZOqI/EMF44RNTR4MNC6Nets/WHzZiAkBLj9dtWREJmHFbfWPXkSiIwEWrVSHYl7mNi6qXNnoLhYdRSeYWJL1FDz5sDIkcDGjaojsb9Nm4ARI4CWLVVHQmQeVmz5VVwsOZBVMLF1U6dO1kpsL1yQrfuY2BI1NG4csHMnUFmpOhL7unAB2L4dGD9edSRE5hIfL6/Nly6pjsR9JSWSA1kFE1s3de4sv1yrOHhQes9x4RhRQxMmSOuaLVtUR2JfW7dKS6P0dNWREJlLQoIsrHRtd28FnLG1KavN2BYUyE4nrlWYRCS6dwd69QI2bFAdiX1t2CA/5549VUdCZC59+shr8759qiNxX3ExZ2xtqXNnWeFbXa06EvcUFMgLS2io6kiIzCc9XZIvTVMdif1omvxs09O5lTfR/xcaCvToIV1DrKC2Fjh9mjO2tuT6pVqlMwIXjhFdX3o68MMP1rodaBVFRcCxYyxDILqexETrzNiWlsqbVSa2NuSahrdKOQITW6LrS02V1jUsR9Dfhg3SCYHb6BJdW9++ktha4Y6Ra20RSxFsyPVLtcICsvJy4NQpLhwjup7gYEm8mNjqb8MGaakWEqI6EiJzSkwEzp61xqZPrsk8ztjaUFgY0KaNNWZsXT3yOGNLdH3p6cCOHWz7pSdXmy+WIRBdX2KifLZCnW1JibxJDQ9XHYn7mNh6wCqbNBQUyK1Arkgmur70dLb90hvbfBE1LSZGJsusUGfravVlpYWgTGw9YJVetgUFQO/eQFCQ6kiIzCs2Vt78sRxBP2zzRdQ0h8M6C8hKSqxVhgAwsfWIVXrZ5ucD/fqpjoLI/CZMANavt8YiDrPTNPlZss0XUdMSE61RimC1HrYAE1uPWGHG9soVmbFlYkvUtDvvlAu3FV5gzG7/fuD4cWDiRNWREJlf375AYSFQU6M6khvjjK3Nde4sfWwvX1YdyfUVFckfChNboqaNGCGLQj/7THUk1rduHdC6tXREIKIbS0wErl4FDh5UHcn1Xb3KxNb2unWTPZ7NvElDfr587ttXbRxEVtCihdw6X7dOdSTW99lnwLhxsnCViG7M1Y7TzHeLyspkIq9bN9WReIaJrQe6dpXPx4+rjeNG8vNlxWVEhOpIiKxh4kRgzx5zv2E1u7Iy4H/+B5g0SXUkRNYQFiYLWM28gMyV67hyH6tgYusBqyS2LEMgcl96OtCsGfD556ojsa4vvpAFYxMmqI6EyDrM3hnBletwxtbGQkOB9u2BEydUR3Jtmgbk5QH9+6uOhMg6IiOBYcNYZ+uLdeuAIUPk+khE7rFCYhsRIesQrISJrYe6dTPvjG1JiWzTxxlbIs9MmiQbNVy4oDoS67l0Cdi4kd0QiDyVmAicPi2lPGZ0/Lj1ZmsBJrYe69rVvImta+EYE1siz0ycCFRXA5s3q47EerZuleSW9bVEnnHdXc3LUxvH9Zw4Yb36WoCJrcfMPGObnw+0bQt06aI6EiJr6dkTuPVWliN447PPgB49gLg41ZEQWYtroffevaojuTbO2AaIbt3kXYwZdypyLRzjrj9Enps0SRaQXb2qOhLrqKuTn9nEibzuEHnK4QAGDDBnYqtpTGwDRrductvtzBnVkTTGjghE3ps8Werdvv5adSTWkZ0tbdKmTFEdCZE1DRgA5OaqjqKxc+eAqiomtgHBrC2/fvoJOHKEiS2RtwYPBjp2BDIzVUdiHZmZQIcO0hGBiDyXlCT5xNmzqiNpyNX9iTW2AcD17sVsLb9cLUOY2BJ5x+mUmce1a81ZamQ2miaJ7ZQp0geYiDw3YIB8NtsCMqv2sAWY2HqsXTsgJMR8M7b5+bI96K23qo6EyLruvhv44QfZiYxuLC8POHYMmDpVdSRE1tWjB9C6tfnqbI8fl+2xb75ZdSSeY2LrIYdDVjIePao6koby8oD4eEluicg7w4fLJgMsR2haZqZ0YRk5UnUkRNbldErbL7MltkePymyt04JZogVDVi82Fvj+e9VRNJSb+/MtDSLyTlCQLCLLzGQ5QlPWrgXuugto3lx1JETWZsYFZN9/L7mOFTGx9UL37rJQyywuXgT27wcGDlQdCZH1TZ0KHD4MFBSojsS8vv0WKCyU0g0i8k1Sklxzzp9XHcnPjhyRXMeKmNh6ITZWpunr6lRHIr75RnpvMrEl8t3o0UB4uMxI0rVlZgJhYcDYsaojIbI+191W1+6hqmkaZ2wDTvfuQE2N9G80g5wcqa3t00d1JETW16KFbDjAOtvry8wE7rxTFpcQkW/i4oBWrcxTZ1tWJv36OWMbQFzvYsxSjpCTI22+uHCMSB933y3lPQcPqo7EfA4dkrtELEMg0kdQENC3r3kSW9caIs7YBpCYGOmOYJYFZDk5LEMg0tP48UCbNsDq1aojMZ/Vq6UMYcIE1ZEQ2YeZFpC5Ju1uuUVtHN5iYuuF4GCgUydzzNj+9BNQVMTElkhPwcEyI7l6Nbsj/JKmyc9kyhS5dUpE+khKkgWZFy6ojkQm7aKigNBQ1ZF4h4mtl8zSGcH1Di85WW0cRHYzc6asVDbLLIoZ5OfLG+mZM1VHQmQvAwbIG0czLCCzckcEgImt18zSyzYnR95VcccxIn2lpcmuO3/9q+pIzGP1atnAYvRo1ZEQ2Ut8vNwFyc5WHYm1OyIATGy9ZpYZ25wcuYXBvdqJ9BUUBMyYAWRkSDu9QFdXB/ztb8D06dyUgUhvzZvLa7kZElvO2Aao2Fjg7Fngxx/VxrFnD+triYwyc6a09duxQ3Uk6u3aBfzwA8sQiIySkgL893+rjaGqCjh1ijO2AalXL/l86JC6GMrLgWPHmNgSGeX226ULCssRpAyhSxdg6FDVkRDZU0oKcOKE2h75rpzGleNYERNbL7l+6UVF6mLYs0c+c+EYkTEcDuDee4E1a4DaWtXRqHP5MvDRR/KzcPJVg8gQKSnyWWU5giuniYtTF4OveInyUliYtPxSmdjm5ACRkdauhSEyu/vuA86dA9avVx2JOl9+CZw5Iz8LIjJGp05A585qyxEKC4EOHYCICHUx+IqJrQ/i4tQntsnJMqtERMZISJBWPMuXq45EneXLZWekfv1UR0Jkb4MHq5+xtfJsLcDE1idxcfLuRgVNk3d1gwerOT9RIJk7F/jiC1lUEWjKy4F164AHHlAdCZH9paTIpNWVK2rOz8Q2wMXFAd99p6YV0KFDcmtw2DD/n5so0MycKS31Vq1SHYn//ed/yl2hWbNUR0JkfykpwMWLwP79/j93XZ3kFlbvi8/E1gdxcUBNjaxi9LedO2URh6vYnIiMExkJTJ4st+QDaYtdTZN/88SJsjEDERlrwADpoa2izra4WJJqztgGMNcvX0Wd7a5dQGIi0KaN/89NFIgeeAA4cODnbiSBIC8P2LePZQhE/hISIq/tKhJbO3REAJjY+qRrVyA4WE1iu3Mn+0kS+dPYsbJqOZAWkS1fDkRFAePHq46E49SDpQAAFfNJREFUKHCo2qihqEh2QIuJ8f+59cTE1gfNmgE9e/p/Adnp01Lby/paIv9p1gyYPVs2KqiuVh2N8WpqZGOK+++XW6NE5B8pKZJknjvn3/MWFgI9elj/752JrY/i4/1f5L1rl3zmjC2Rfz3wgGyjvWaN6kiM9/HHQEUFyxCI/E3VRg379wN9+vj3nEZgYuujhASgoMC/C0p27ZKtLbt08d85iUju0IweDSxbpjoS4739NpCaCvTurToSosDSowdw000/T2L5g6ZJLpOQ4L9zGoWJrY8SEoDz52U1ob/s3MkyBCJV5s0Ddu+WhVV2tW+fXGfmzVMdCVHgcTiA4cOBrCz/nbO0VO7QMLGl+kFQUOCf8128COTmsgyBSJWJE2XbSzvP2i5bBkRHS4szIvK/ESOkFKGmxj/nc+UwTGwJ3boBYWH+S2xdO5JwxpZIjaAg4O//XjYu8PfiDn84f142onjkEVkhTUT+N3y4JLU5Of45X0EBEBoK3HKLf85nJCa2PnI4pNjaX4ntzp3Su9YOBd5EVvXww/IGc+VK1ZHo74MP5AX1kUdUR0IUuPr2lUkzf5UjFBTIYninDbJCG/wT1HMtIPOHXbuA22+X1kNEpEaHDsC0aXLLvq5OdTT60TT5N02ZAnTsqDoaosDVrJncmfVnYmuXCTMmtjpISAAOHgQuXzb2PFeuSGLLMgQi9R59VPpJb9qkOhL9bNkivSwffVR1JEQ0YoS85vsjt/j2W3vU1wJMbHWRmCgDz+iNGnJzgZ9+AkaNMvY8RNS0oUOBpCRg6VLVkehn6VK5BZqaqjoSIho1CqiqMr7O9rvvpPyIiS3V699fam1zc409z5YtQOvWwMCBxp6HiJrmcABPPSV/l0b/7ftDXh6wcaP8mxwO1dEQUVISEB4u1xgj7dnz8/nsgImtDsLCgFtvNf5d1datMpPClcpE5nD33UBsLPDqq6oj8d3SpbJH/IwZqiMhIkDqbEeO9E9i27MnEBFh7Hn8hYmtTpKTf37XY4Tqaqm1YRkCkXk0awYsWABkZgKHD6uOxntHjwIZGcCTT1p/n3giOxk1SjaEuXjRuHPk5EgOYxdMbHWSnAx88w1QW2vM8b/+WpLb0aONOT4ReefXvwbatwf+8AfVkXjv9deByEhg7lzVkRDRL40eLXnFzp3GHP/KFSlDYmJLjQwcKMXX+/cbc/xNm2TvaLsUdxPZRatWwG9+A6xYAZSVqY7Gc+XlwPvvA489BoSEqI6GiH7ptttkF0Cjuq98+61Mmtlp7Q4TW5307Su3JY0qR9iwARg/3h7Nk4ns5h//UWrfX39ddSSee/NNWSw2b57qSIjo/3M45LV/wwZjjp+TI+fo39+Y46vANEknISGya4cRC8hKSqTMIT1d/2MTke/atgXmzwfeekv+Xq2irAz4059kxrldO9XRENG1pKcDBw4AJ07of+w9e4DevaXjkl0wsdVRSorUwurtyy9lpvbv/k7/YxORPp58Ut7gvvyy6kjct2QJ0KIFsHCh6kiI6HrGjpU7wkbM2n79NTB4sP7HVYmJrY5GjJB6lfJyfY+7fr0MPM6oEJlXeDjw298C//Ef1uiQcPQo8N57wNNPy4wzEZlTRAQwZIj+iW1FhWyla7cNWZjY6mjECPm8Y4d+x6ytBTZvZhkCkRXMmwfcfDPw4ouqI2na4sXyZvnxx1VHQkRNSU+XXKC6Wr9j7twJaNrPuYtdMLHVUZcu0uA8K0u/Y27dKtvo3nWXfsckImO0agW88AKwejWwb5/qaK7vwAHgL38Bnn+enRCIrOCuu4ALF/TdrCEr6+e8xU6Y2OpsxAh9E9u1a2VnI7b5IrKGuXPlb3b+fJkNMRtNk3rgmBjgoYdUR0NE7ujdG4iLk5xAL1lZkrPYbQttJrY6S00F8vOB8+d9P9bVq8AnnwBTp9pv4BHZVfPmwJ//LHdbMjJUR9NYZibwX/8lMbZooToaInKHwyG5wKefyqYKvqqsBPbutV8ZAsDEVnepqTIj8tVXvh9r1y5ZiDZ1qu/HIiL/SU+Xv9v58/V5k6uXykrgiSfktuadd6qOhog8MXUqcPasPut4srJk8sxuC8cAJra6i40FevYEvvjC92N9+CHQsSMwaJDvxyIi//rjHyWRNNNCssWLZSX0n/6kOhIi8lRSEtC1q+QGvvriC6B7d6BXL9+PZTZMbA1w550yaHypr6utBf72N+C++7jbGJEVdekiSe2//quUJ6m2b58ktC+8AHTrpjoaIvKUwyE5QUYGUFPj/XE0Dfj8c8lV7FjmyJTJAHfeCZw86duL2Zdfyi2H2bP1i4uI/OuJJ2TRx4MPApcvq4vj8mVZKNarF/BP/6QuDiLyzf33A+fO+XZXeP9+4Icf7FuOxMTWAMOGAW3ayDsib33wAdCvH7shEFlZ8+bAihUyW6pyR7Lf/U4WiixfzgVjRFZ2221SkvCXv3h/jM8/ly107bhwDGBia4gWLYBx46SjgTfOngXWreNsLZEdJCdLv9hXXtF38xZ3ff21JNXPPWe/rTOJAtHs2TJje/q0d8//9FPZprdlS33jMgsmtga5916ZITlwwPPn/tu/Sd3Lr36lf1xE5H/PPit3cu691/sXI2+UlwMzZgApKcCiRf47LxEZZ9YsIChItsT2VFERkJ0NzJypf1xmwcTWIHfcAURGAitXeva8y5eBt9+WgXvTTcbERkT+FRQki0GvXgXuuUcWhxrt8mV58aqtlcUmzZsbf04iMl67djLxtWyZ59eSlSuBiAhg4kRjYjMDJrYGadlSVi+uWuVZM+VPPgGKi4Hf/Ma42IjI/6KjgY8+kv7U//APxu5KpmnAo49Kr8oPPwQ6dTLuXETkf48/DpSWyoYr7rp6VWpzZ84EgoONi001QxPbsrIyPPPMM0hLS0NYWBicTie2b9/u0TFKSkowY8YMtG3bFuHh4Zg8eTKOHj1qUMT6mjNHBt6GDe59f12dLPJISwMSEw0NjYgUGD4ceP99WcT1/PPGneell4B//3cpaxo50rjzEJEaffpInezvfy8Jqzs2bpSJszlzDA1NOUMT28LCQrz22msoLS1F4v9lag4PmqZVVVUhLS0NO3bswHPPPYeXXnoJeXl5SE1NRUVFhVFh62bAAGDIEFk04s7sTEaGtAhTuXqaPLN69WrVIZDF/OpXwNKlcl1YssT9mVt3x9rvfy+J7b/8C/DrX/sQKAUsXtes4Z//GSgoAP7616a/V9PkmjNoEDBwoPGxqWRoYpucnIyKigoUFhZi/vz5Hj9/2bJlOHz4MD7//HMsWLAATzzxBDZu3IjS0lK8/vrrBkSsL4dDGrRnZ8ve7DdSWyuLOyZOBIYO9U985Du+AJA3FiyQpPb554Enn5S7NU1paqzV1clxn31WEtunn9YpWAo4vK5ZQ0oKMHmyXEea2rBhyxYpg1q82J6bMvySoYlt69atERER4fXz16xZg0GDBiEpKan+sbi4OIwePRof6rGnnB+MHQvcfrskrTeqtV28GDhxQkoRiMj+nntOFor+8Y/ApEmy1a23zp0DpkwB3ngD+POfZXcxIrK/3/1ONoS6UWnT1auSgwwaBIwf77/YVDHt4rG6ujrs27cPycnJjb42cOBAHDlyBBcuXFAQmWccDuAPfwDy8uS2wbVs3y63DV9+WepmiCgwPPqoNEvfvVs2ZPFmU5f16+W5WVnSn/Kxx/SPk4jMqXdvKTFYulRmZa/llVeAnBzJRew+WwuYOLGtqKhAbW0toqOjG33N9djJkyf9HZZXhgyRW4NLlgBr1jT82s6dcishNRVYuFBNfESkzoQJ8sb3ttukFGncOElSb1R7q2ly7UhPl9aCcXFyDDu38CGia3vySWDMGODuu+Xa8UuffCL5xwsvyOLVQBDk7jdqmoaapoo4/k+wDn0kLl26BABoeY2tMVzHd33PtZ538ODBpk/i+h53vtdHrher6dMlkU1Olv2a166VWdrFi4FvvjE8DH358ednVufPn8fevXtVh2F+HCtNeuUVYNQoabqemiotuoYOlRmZyEjg6NHzWLx4LwoLpVauuBi45RZZLDZ2rJQyWGBNrRocfx4J6OuaRcfK889Ljf2YMVKWlJgom0StXSudliZMkP83nAc/P1eedq1czieam7Zt26Y5HA63PoqKiho9/6OPPtIcDoe2fft2t85XXl6uORwObcmSJY2+9vbbb2sOh0M7dOhQo6+tWrVKA8APfvCDH/zgBz/4wQ+Tf6xatcrdVNQtbs/Y9u7dGytWrHDre6Oiotw97HVFRkaiZcuWKC0tbfQ112MdO3Zs9LVx48Zh1apViImJQatWrXyOg4iIiIj0denSJRw7dgzjxo3T9bhuJ7YdOnTA7NmzdT35jTidTiQkJCAnJ6fR17KzsxEbG4vQ0NBGX2vfvj1mzZrljxCJiIiIyEtDDehvaprFYydOnEBhYWGDx6ZNm4acnBzk5ubWP1ZUVIRt27Zh+vTp/g6RiIiIiEzMoWlG7lgOLFmyBABw4MABZGRkYO7cuYiJiQEALFq0qP77Ro4ciaysLNT9olN5VVUV+vfvj8rKSixYsABBQUF44403oGka8vPz0a5dOyNDJyIiIiILMTyxdTqdcDgc0DSt/jMgW+te/cUGx2lpacjKymrwGACUlJRg/vz52LhxI+rq6pCWloY333wT3bt3NzJsIiIiIrIYwxNbIiIiIiJ/ME2NLRERERGRLyyd2JaVleGZZ55BWloawsLC4HQ6sX37do+OUVJSghkzZqBt27YIDw/H5MmTcfToUYMiJiv78ccf8cgjj+Cmm25C69atMWrUKOTl5bn13MWLF8PpdDb6YEu6wFZTU4Onn34aHTt2REhICFJSUrB582a3nuvLeKTA4+1YW7FixTWvXU6nE6dPn/ZD5GQlFy5cwIsvvojx48cjMjISTqcTK1eudPv5elzX3G73ZUaFhYV47bXX0KtXLyQmJmL37t1weLARclVVFdLS0lBZWYnnnnsOQUFBePPNN5Gamor8/HxERkYaGD1ZSV1dHe644w7s27cPTz31FNq1a4dly5Zh5MiRyM3NRY8ePdw6zrvvvovWrVvX/3+zZs2MCpksYM6cOcjMzMT8+fPRs2dPLF++HBMmTMC2bdtu2AZHr/FIgcPbseby8ssv45ZbbmnwWHh4uFHhkkWVl5fj5ZdfRrdu3dCvXz989dVXbudlul3XdN3uwc8qKyu1c+fOaZrm+c5mmqZpr776quZwOLQ9e/bUP1ZYWKgFBQVpzz77rO7xknVlZGRoDodDy8zMrH+svLxca9u2rXbfffc1+fwXX3xRczgc2tmzZ40MkywkOztbczgc2uuvv17/WHV1tdajRw9tyJAhN3yur+ORAosvY2358uWaw+HQcnNzjQ6TbKCmpkY7deqUpmmatmfPHs3hcGgrV65067l6XdcsXYrQunVrREREeP38NWvWYNCgQUhKSqp/LC4uDqNHj8aHH36oR4hkE2vWrEFUVBSmTp1a/1j79u0xY8YMfPrpp7h8+bJbx6mrq8NPP/1U3x2EAteaNWsQFBSERx55pP6xli1b4sEHH8Tu3btRUlJyw+fqMR4pMPgy1lw0TUNlZWWjzkVEv9SiRQvcfPPNAODx65xe1zVLJ7a+qKurw759+5CcnNzoawMHDsSRI0dw4cIFBZGRGeXl5WHAgAGNHh84cCAuXryIQ4cOuXWc7t27IyIiAm3atMH999/PGrUAlpeXh169ejUoTQFkTAFAfn7+DZ+rx3ikwODLWHNJS0tDeHg4QkNDcdddd+Hw4cOGxEqBS6/rWsAmthUVFaitrUV0dHSjr7keO3nypL/DIpMqLS31aaxERkbisccew3vvvYfMzEw89NBDyMjIwPDhw1FZWWlIzGRuvowpX8cjBRZfxktoaCgeeOABLFu2DJ988gmeeuopbNmyBUOGDEFxcbFhMVPg0eu6ZprFY5qmoaamxq3vDQ4O9vl8ly5dAiC3Y653fNf3kL14M9aqq6t9GiuPP/54g/+fMmUKBg0ahFmzZmHZsmV4+umn3YqH7OPSpUtejylfxyMFFl/G2vTp0xtsYT9p0iSMGzcOI0aMwCuvvIJ33nlH/4ApIOl1XTPNjO327dsREhLi1ocet9lcbZauleBUV1c3+B6yF2/GWqtWrXQfKzNnzkRUVBS2bNni2z+ILMmXMWXEeCT70nu8DB06FIMHD3a7NR2RO/Qap6aZse3duzdWrFjh1vdGRUX5fL7IyEi0bNkSpaWljb7meqxjx44+n4fMx5uxFh0dfc3bIL6Olc6dO6OiosKr55K1+TKmjBqPZE9GjJfOnTuzlpt0pdc4NU1i26FDB8yePdtv53M6nUhISEBOTk6jr2VnZyM2NhahoaF+i4f8x5ux1q9fP+zYsQOapjXoyZednY3Q0FD06tXL4zg0TcOxY8cadOWgwNG/f3989dVXqKysRFhYWP3j2dnZAGTMXY8R45Hsy5exdj3ff/89brrpJt1iJNLrumaaUgSjnThxAoWFhQ0emzZtGnJycpCbm1v/WFFREbZt29agpoho2rRpOHXqFNauXVv/2JkzZ/DRRx9h4sSJaN68ef3j1xpr5eXljY75zjvv4MyZMxg/frxxgZNpTZs2DVevXsV7771X/1hNTQ2WL1+OlJQUdOrUCYDssFhYWIgrV640eK6745HIl7F2rWvX+vXrsXfvXl67yGtGXtccmsUbai5ZsgQAcODAAWRkZGDu3LmIiYkBACxatKj++0aOHImsrCzU1dXVP1ZVVYX+/fujsrISCxYsQFBQEN544w1omob8/Hy0a9fOr/8WMq+6ujoMGzYM+/fvx8KFC+t3RCkuLkZOTg569uxZ/73XGmshISG499570adPHwQHB2Pnzp3IyMhAv379sGvXLl0WRJL13HPPPfj4448xf/58xMbGYuXKldizZw+2bNmCYcOGAZAdoz744AMcO3YMXbt2BeDZeCQCvB9rPXv2xIABA5CUlITw8HDs3bsX77//Pjp16oScnBzO2lIjb731Fn788UecPHkS7777LqZOnVp/V+Dxxx9HmzZtjL2uub2Vg0k5HA7N6XQ2+Oz6718aOXJko8c0TdOKi4u16dOna+Hh4VpYWJg2adIk7ciRI/4Knyzk3Llz2kMPPaS1b99eCw0N1dLS0q65G8+1xtrDDz+sxcfHa23atNFatGih9erVS/vtb3+rVVVV+St8MqHq6mpt4cKFWnR0tBYcHKwNHjxY27hxY4PvmTNnjuZ0OrXjx483eNzd8Uikad6PtUWLFmn9+/fXIiIitBYtWmgxMTHavHnztNOnT/v7n0AWERMT0yAX+2WO5hpbRl7XLD9jS0REREQEBFCNLRERERHZGxNbIiIiIrIFJrZEREREZAtMbImIiIjIFpjYEhEREZEtMLElIiIiIltgYktEREREtsDEloiIiIhsgYktEREREdkCE1siIiIisgUmtkRERERkC0xsiYiIiMgW/hcCH4ooyRXFhAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f77b6d05dd8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-1, 1, 401);\n",
    "y = chebyshev(x, 6);\n",
    "z = chebyshev_zeros(6)\n",
    "plot(x, y)\n",
    "axhline(y=0.0, color=\"black\")\n",
    "[axvline(x=zz, color=\"red\") for zz in z];\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again there are mutating versions of this function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       " -0.899519 \n",
       " -0.537495 \n",
       " -0.0136203\n",
       "  0.514423 \n",
       "  0.887668 "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = zeros(5)\n",
    "jacobi_zeros!(5, a, b, z)\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types other than `Float64`\n",
    "\n",
    "Most times, calculations will be carried out using `Float64` because that is the most useful datatype. Most functions can be used with other data types, including `Float32`, `BigFloat` and, except when calculating zeros of polynomials, `Rational{T}`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.11098426440730691"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobi(float32(0.5), 8, 0.5, 1.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "214832820407//506623120463"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chebyshev(23//47, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.770638984160155424568808763332988903749347442526164591900368406181365041596503e+00 with 256 bits of precision"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "djacobi(BigFloat(0.6), 10, 0.5, -0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{BigFloat,1}:\n",
       " -1e+00                                                                               \n",
       " -8.717401485096066153374457612206634381037806696769833549194152855738989940929645e-01\n",
       " -5.917001814331423021445107313979531899457009895173324967422595914701481800491344e-01\n",
       " -2.092992179024788687686572603453512552955454050866810988908466923221309236462841e-01\n",
       "  2.092992179024788687686572603453512552955454050866810988908466923221309236462841e-01\n",
       "  5.917001814331423021445107313979531899457009895173324967422595914701481800491344e-01\n",
       "  8.717401485096066153374457612206634381037806696769833549194152855738989940929645e-01"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jacobi_zeros(7, 1, -1, BigFloat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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